Sensitivity to habitable planets in the \textit{Roman} microlensing survey

We study the \textit{Roman} sensitivity to exoplanets in the Habitable Zone (HZ). The \textit{Roman}~efficiency for detecting habitable planets is maximized for three classes of planetary microlensing events with close caustic topologies. (a) The events with the lens distances of $D_{\rm l} \gtrsim 7$ kpc, the host lens masses of $M_{\rm h}\gtrsim 0.6M_{\odot}$. By assuming Jupiter-mass planets in the HZs, these events have $q\lesssim 0.001$ and $d\gtrsim 0.17$ ($q$ is their mass ratio and $d$ is the projected planet-host distance on the sky plane normalized to the Einstein radius). The events with primary lenses, $M_{\rm h} \lesssim 0.1 M_{\odot}$, while their lens systems are either (b) close to the observer with $D_{\rm l}\lesssim 1$ kpc or (c) close to the Galactic bulge, $D_{\rm l}\gtrsim 7$ kpc. For Jupiter-mass planets in the HZs of the primary lenses, the events in these two classes have $q\gtrsim 0.01$, $d\lesssim 0.04$. The events in the class (a) make larger caustics. By simulating planetary microlensing events detectable by \textit{Roman},~we conclude that the \textit{Roman}~efficiencies for detecting Earth- and Jupiter-mass planets in the Optimistic HZs (OHZs, which is the region between $[0.5,~2]$ AU around a Sun-like star) are $0.01\%$ and $5\%$, respectively. If we assume that one exoplanet orbits each microlens in microlensing events detectable by \textit{Roman}~( i.e., $\sim 27000$ ),~this telescope has the potential to detects $35$ exoplanets with the projected planet-host distances in the OHZs with only one having a mass $\lesssim 10M_{\oplus}$. According to the simulation, $27$ of these exoplanets are actually in the OHZs.